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IMA Journal of Mathematical Control and Information 1990 7(4):339-349; doi:10.1093/imamci/7.4.339
© 1990 by Institute of Mathematics and its Applications
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Exponential Stabilization using Nondifferential Gain Adaptation

ACHIM ILCHMANN and DAVID H. OWENS

1Institut für Angewandte Mathematik, Universität Hamburg D-2000 Hamburg 13, Germany
1University of Exeter, School of Engineering North Park Road, Exeter EX4 4QF, UK

A new type of adaptive high-gain stabilizer for classes of linear time-invariant state-space systems is presented. The classes cover multi-input multi-output systems where the state dimension is not known. Only standard assumptions of minimum phase and known (respectively unknown) sign are required. The controller is of nondifferential form and ensures exponential decay of the trajectory. In the case where the sign of the high-frequency gain is not known, a new type of switching function is introduced that guarantees switching convergence independent of gain adaptation.


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